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1. 1. ONE-SCHOOL.NET http://www.one-school.net/notes.html 1 Physics Equation List :Form 4 Introduction to Physics Relative Deviation Mean DeviationRelative Deviation = 100% Mean Value Prefixes Prefixes Value Standard form Symbol Tera 1 000 000 000 000 1012 T Giga 1 000 000 000 109 G Mega 1 000 000 106 M Kilo 1 000 103 k deci 0.1 10-1 d centi 0.01 10-2 c milli 0.001 10-3 m micro 0.000 001 10-6 nano 0.000 000 001 10-9 n pico 0.000 000 000 001 10-12 p Units for Area and Volume 1 m = 102 cm (100 cm) 1 m2 = 104 cm2 (10,000 cm2 ) 1 m3 = 106 cm3 (1,000,000 cm3 ) 1 cm = 10-2 m ( 1 100 m ) 1 cm2 = 10-4 m2 ( 21 10,000 m ) 1 cm3 = 10-6 m3 ( 31 1,000,000 m )
2. 2. ONE-SCHOOL.NET http://www.one-school.net/notes.html 2 Force and Motion Average Speed Total DistanceAverage Speed Total Time = Velocity sv t = v = velocity (ms-1 ) s = displacement (m) t = time (s) Acceleration v u a t = a = acceleration (ms-2 ) v = final velocity (ms-1 ) u = initial velocity (ms-1 ) t =time for the velocity change (s) Equation of Linear Motion Linear Motion Motion with constant velocity Motion with constant acceleration Motion with changing acceleration s v t = atuv += tvus )( 2 1 += 2 2 1 atuts += asuv 222 += Using Calculus (In Additional Mathematics Syllabus) u = initial velocity (ms-1 ) v = final velocity (ms-1 ) a = acceleration (ms-2 ) s = displacement (m) t = time (s)
3. 3. ONE-SCHOOL.NET http://www.one-school.net/notes.html 3 Ticker Tape Finding Velocity: velocity number of ticks 0.02s s = 1 tick = 0.02s Finding Acceleration: v u a t = a = acceleration (ms-2 ) v = final velocity (ms-1 ) u = initial velocity (ms-1 ) t = time for the velocity change (s) Graph of Motion Gradient of a Graph The gradient 'm' of a line segment between two points and is defined as follows: Change in y coordinate, Gradient, Change in x coordinate, y m x or y m x = =
4. 4. ONE-SCHOOL.NET http://www.one-school.net/notes.html 4 Displacement-Time Graph Velocity-Time Graph Gradient = Velocity (ms-1 ) Gradient = Acceleration (ms-2 ) Area in between the graph and x-axis = Displacement Momentum p m v= p = momentum (kg ms-1 ) m = mass (kg) v = velocity (ms-1 ) Principle of Conservation of Momentum 1 1 2 2 1 1 2 2m u m u m v m v+ = + m1 = mass of object 1 (kg) m2 = mass of object 2 (kg) u1 = initial velocity of object 1 (ms-1 ) u2 = initial velocity of object 2 (ms-1 ) v1 = final velocity of object 1 (ms-1 ) v2 = final velocity of object 2 (ms-1 ) Newtons Law of Motion Newtons First Law In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line).
5. 5. ONE-SCHOOL.NET http://www.one-school.net/notes.html 5 Newtons Second Law mv mu F t F ma= The rate of change of momentum of a body is directly proportional to the resultant force acting on the body and is in the same direction. F = Net Force (N or kgms-2 ) m = mass (kg) a = acceleration (ms-2 ) Implication When there is resultant force acting on an object, the object will accelerate (moving faster, moving slower or change direction). Newtons Third Law Newton's third law of motion states that for every force, there is a reaction force with the same magnitude but in the opposite direction. Impulse Impulse Ft= Impulse mv mu= F = force (N) t = time (s) m = mass (kg) v = final velocity (ms-1 ) u = initial velocity (ms-1 ) Impulsive Force mv mu F t = F = Force (N or kgms-2 ) t = time (s) m = mass (kg) v = final velocity (ms-1 ) u = initial velocity (ms-1 ) Gravitational Field Strength F g m = g = gravitational field strength (N kg-1 ) F = gravitational force (N or kgms-2 ) m = mass (kg) Weight W mg= W = Weight (N or kgms-2 ) m = mass (kg) g = gravitational field strength/gravitational acceleration (ms-2 )
6. 6. ONE-SCHOOL.NET http://www.one-school.net/notes.html 6 Vertical Motion If an object is release from a high position: The initial velocity, u = 0. The acceleration of the object = gravitational acceleration = 10ms-2 (or 9.81 ms-2 ). The displacement of the object when it reach the ground = the height of the original position, h. If an object is launched vertically upward: The velocity at the maximum height, v = 0. The deceleration of the object = -gravitational acceleration = -10ms-2 (or -9.81 ms-2 ). The displacement of the object when it reach the ground = the height of the original position, h. Lift In Stationary R mg= When a man standing inside an elevator, there are two forces acting on him. (a) His weight which acting downward. (b) Normal reaction (R), acting in the opposite direction of weight. The reading of the balance is equal to the normal reaction.
7. 7. ONE-SCHOOL.NET http://www.one-school.net/notes.html 7 Moving Upward with positive acceleration Moving downward with positive acceleration R mg ma= + R mg ma= Moving Upward with constant velocity Moving downward with constant velocity. R mg= R mg= Moving Upward with negative acceleration Moving downward with negative acceleration R mg ma= R mg ma= +
8. 8. ONE-SCHOOL.NET http://www.one-school.net/notes.html 8 Smooth Pulley With 1 Load T1 = T2 Moving with uniform speed: T1 = mg Stationary: T1 = mg Accelerating: T1 mg = ma With 2 Loads Finding Acceleration: (If m2 > m1) m2g m1g = (m1+ m2)a Finding Tension: (If m2 > m1) T1 = T2 T1 m1g = ma m2g T2 = ma Vector Vector Addition (Perpendicular Vector) Magnitude = 2 2 x y+ Direction = 1 | | tan | | y x Vector Resolution | | | | sinx p = | | | | cosy p =
9. 9. ONE-SCHOOL.NET http://www.one-school.net/notes.html 9 Inclined Plane Component parallel to the plane = mgsin Component perpendicular to the plane = mgcos Forces In Equilibrium 3T mg= 2 sinT mg = 2 1cosT T = 1 tanT mg = 3T mg= 2 1cos cosT T = 2 1sin sinT T mg + = Work Done cosW Fx = W = Work Done (J or Nm) F = Force (N or kgms-2 ) x = displacement (m) = angle between the force and the direction of motion (o ) When the force and motion are in the same direction. W Fs= W = Work Done (J or Nm) F = Force (N or kgms-2 ) s = displacement (m)
10. 10. ONE-SCHOOL.NET http://www.one-school.net/notes.html 10 Energy Kinetic Energy 21 2 KE mv= EK = Kinetic Energy (J) m = mass (kg) v = velocity (ms-1 ) Gravitational Potential Energy PE mgh= EP = Potential Energy (J) m = mass (kg) g = gravitational acceleration (ms-2 ) h = height (m) Elastic Potential Energy 21 2 PE kx= 1 2 PE Fx= EP = Potential Energy (J) k = spring constant (N m-1 ) x = extension of spring (m) F = Force (N) Power and Efficiency Power W P t = E P t = P = power (W or Js-1 ) W = work done (J or Nm) E = energy change (J or Nm) t = time (s) Efficiency Useful Energy Efficiency = 100% Energy Or Power Output Efficiency = 100% Power Input Hookes Law F kx= F = Force (N or kgms-2 ) k = spring constant (N m-1 ) x = extension or compression of spring (m)
11. 11. ONE-SCHOOL.NET http://www.one-school.net/notes.html 11 Force and Pressure Density m V = = density (kg m-3 ) m = mass (kg) V = volume (m3 ) Pressure F P A = P = Pressure (Pa or N m-2 ) A = Area of the surface (m2 ) F = Force acting normally to the surface (N or kgms-2 ) Liquid Pressure P h g= h = depth (m) = density (kg m-3 ) g = gravitational Field Strength (N kg-1 ) Pressure in Liquid atmP P h g= + h = depth (m) = density (kg m-3 ) g = gravitational Field Strength (N kg-1 ) Patm = atmospheric Pressure (Pa or N m-2 ) Gas Pressure Manometer atmP P h g= + Pgas = Pressure (Pa or N m-2 ) Patm = Atmospheric Pressure (Pa or N m-2 ) g = gravitational field strength (N kg-1 )
12. 12. ONE-SCHOOL.NET http://www.one-school.net/notes.html 12 U=tube 1 1 2 2h h = Pressure in a Capillary Tube Pgas = gas pressure in the capillary tube (Pa or N m-2 ) Patm = atmospheric pressure (Pa or N m-2 ) h = length of the captured mercury (m) = density of mercury (kg m-3 ) g = gravitational field strength (N kg-1 ) Barometer Pressure in unit cmHg Pressure in unit Pa Pa = 0 Pa = 0 Pb = 26 Pb = 0.261360010 Pc = 76 Pc = 0.761360010 Pd = 76 Pd = 0.761360010 Pe = 76 Pe = 0.761360010 Pf = 84 Pf = 0.841360010 (Density of mercury = 13600kgm-3 )
13. 13. ONE-SCHOOL.NET http://www.one-school.net/notes.html 13 Pascals Principle 1 2 1 2 F F A A = F1 = Force exerted on the small piston A1 = area of the small piston F2 = Force exerted on the big piston A2 = area of the big piston Archimedes Principle Weight of the object, 1 1W V g= Upthrust, 2 2F V g= 1 = density of wooden block V1 = volume of the wooden block 2 = density of water V2 = volume of the displaced water g = gravitational field strength Density of water > Density of wood F = T + W Vg T mg = + Density of Iron > Density of water T + F = W Vg T mg + =
14. 14. ONE-SCHOOL.NET http://www.one-school.net/notes.html 14 Heat Heat Change Q mc= m = mass (kg) c = specific heat capacity (J kg-1 o C-1 ) = temperature change (o ) Electric Heater Mixing 2 Liquid Energy Supply, E Pt= Energy Receive, Q mc= Energy Supply, E = Energy Receive, Q Pt mc= E = electrical Energy (J or Nm) P = Power of the electric heater (W) t = time (in second) (s) Q = Heat Change (J or Nm) m = mass (kg) c = specific heat capacity (J kg-1 o C-1 ) = temperature change (o ) Heat Gain by Liquid 1 = Heat Loss by Liquid 2 1 1 1 2 2 2m c m c = m1 = mass of liquid 1 c1 = specific heat capacity of liquid 1 1 = temperature change of liquid 1 m2 = mass of liquid 2 c2 = specific heat capacity of liquid 2 2 = temperature change of liquid 2 Specific Latent Heat Q mL= Q = Heat Change (J or Nm) m = mass (kg) L = specific latent heat (J kg-1 ) Boyles Law 1 1 2 2PV PV= (Requirement: Temperature in constant) Pressure Law 1 2 1 2 P P T T = (Requirement: Volume is constant)
15. 15. ONE-SCHOOL.NET http://www.one-school.net/notes.html 15 Charless Law 1 2 1 2 V V T T = (Requirement: Pressure is constant) Universal Gas Law 1 1 2 2 1 2 PV PV T T = P = Pressure (Pa or cmHg .) V = Volume (m3 or cm3 ) T = T